Download PPTX

Systems Biology for Clinical Decision
Support Systems
• Outlines:
– Machine learning; bridge between systems biology /
medicine, and clinical decision support systems
– Brief introduction to fundamental techniques in
machine learning
• Clustering/unsupervised learning
• Classification/supervised learning
2014
Dept of Comp Med & Bioinf, Kayvan
Najarian
1
Big Picture
• A “holistic” approach
Molecular /
Cellular
Data
Modeling /
Machine
Learning
Biomedical
Signals
Raw
Clinical
Data
Biomedical
Images/Videos
Electronic
Health Records
(HER)
2014
Feature
Extraction
Features
Signal
Processing
& Feature
Extraction
Image
Processing
& Feature
Extraction
Feature
Extraction
Features
Features
Integrated
Features
Machine
Learning
Recommendations
/ Predictions
Features
Dept of Comp Med & Bioinf, Kayvan
Najarian
2
Big Picture (cont’d)
2014
Dept of Comp Med & Bioinf, Kayvan
Najarian
3
Machine Learning
• Learning / extracting patterns from data
• Applied when data are analyzed for:
–
–
–
–
Pattern recognition
Classification and clustering
Prediction
Forming recommendation
• Inspired by biology
• Unlike modeling methods that conform to the physical
laws of the systems being model, machine learning relies
on pattern in training data
2014
Dept of Comp Med & Bioinf, Kayvan
Najarian
4
Supervised vs. Unsupervised Learning *
• Supervised Learning / Classification
– Training data are labeled, i.e. the output class of all training data
are given
–
Example: predicting if a sequence is an a-helix or a b-sheet
•
Training set:  Seq1   helix , Seq2  b  sheet , Seq3   helix , Seq4  b  sheet 
• Classification: Seq5  ?
• Unsupervised Learning / Clustering
–
–
–
Training data are not labeled
Output classes must be generated during training
Similarity across features of training examples creates different
classes
* Reinforcement learning is not discussed here
2014
Dept of Comp Med & Bioinf,
Kayvan Najarian
5
Supervised vs Unsupervised Learning (cont’d)
–
Example (visual insight via scattered plot): Identification of tumor types
• Input features: Size of Tumor &
Rate of Growth
• Training data create natural clusters
– No specific labels are available
– Assume all tumors are cancerous
• From graph:
Class #1: small size of tumor with small rate of growth
Class #2: small size of tumor with large rate of growth
Class #3: medium size of tumor with medium rate of growth
Class #4: large size of tumor with small rate of growth
100
500
Size of Tumor
1000
• Classification: a tumor with SOT=600 & ROG=12% is mapped to Class #3
– Classification is performed based on clustering results
• Each clustering algorithm results to a classification technique
2014
Dept of Comp Med & Bioinf,
Kayvan Najarian
6
Clustering
– General concept of clustering:
• Assume there are K classes
• Represent each class with its center
– Start with some random initial centers
• Find the best centers for classes, i.e.
optimize the centers
Expression Level After Treatment
• The simplest clustering algorithm: K-means
• K-means clustering algorithm
Expression Level Before Treatment
– In classification phase:
• Find the distance of a new pattern from all centers
• Find the center whose distance from the the new pattern is minimal
• Classify the new pattern to the class whose center has minimal
distance from the pattern
2014
Dept of Comp Med & Bioinf,
Kayvan Najarian
7
Clustering (cont’d)
– Mathematical formulation:
• Randomly initialize the centers m0, m1,…, mK-1.
• Find the distance of all samples x0, x1,…, xn-1
from all centers m0, m1,…, mK-1, i.e. for all
0in-1 and 0jK-1 find:
d ( xi , m j )  xi  m j
• Form classes j = 1,2,…, K-1, by assigning
each sample to the closet center,
i.e. put together all examples whose
distance to center j is minimal to
form class j.
• Then find the new centers by finding the sample
that is the closet sample to the average of all
samples in the class, i.e., new mj = average( all examples in class j)
2014
Dept of Comp Med & Bioinf,
Kayvan Najarian
8
Clustering (cont’d)
• Repeat the previous two steps, unless during
the last iteration, no example has changed
its class
– Advantages of K-means
• Simple and fast
• Works on a wide range of simple data
– Disadvantages:
• Assumes that the number of classes is available
• Depends on initial centers
• Unable to cluster complicated data
– Solutions:
• ISODATA
• Kohonen self-organizing map
2014
Dept of Comp Med & Bioinf,
Kayvan Najarian
9
Classification with KNN
• Simplest type of classification
algorithm: K Nearest Neighbors
– General concept:
• Calculate the distance of the new
example to all known examples (and
not just centers)
• For each class, find the K known
examples that belong to the class and
have the minimal distance from the
new pattern (among all examples
belonging to this class)
• Find the total distance of all the
examples of each class and do this
for all of the classes
• The class with minimum total
distance wins the new pattern
2014
Dept of Comp Med & Bioinf,
Kayvan Najarian
10
Classification with KNN (cont’d)
• The main advantage of KNN is that, just like neural
networks, it does not require the knowledge of probability
distribution of the classes
• KNN is much less complex and computationally intensive
than connectionist methods such as neural networks and
support vector machines
• More computationally-intensive classifiers exist that do
require the exact knowledge or at least an accurate
estimation of the distributions
2014
Dept of Comp Med & Bioinf,
Kayvan Najarian
11
Introduction to Connectionist Models
• Why connectionist models?
– Algorithms developed over centuries do not fit the complexity of
real world problem
– The human brain: most sophisticated computer suitable for solving
extremely complex problems
• Historical knowledge on human brain
– Phineas Gage’s Story
• In a rail accident, a metal bar was shot
through the head of Mr. Phineas
P. Gage at Cavendish, Vermont,
Sept 14, 1848
– Iron bar was 3 feet 7 inches long
and weighed 13 1/2 pounds.
It was 1 1/4 inches in diameter http://www.boston.com/news/local/massachusetts/articles/2009/07/2
2/newly_discovered_image_offers_fresh_insights_about_1848_medi
at one end
cal_miracle/ (From the collection of Jack and Beverly Wilgus)
2014
Dept of Comp Med & Bioinf,
Kayvan Najarian
12
Introduction to Connectionist Models (cont’d)
• He survived the accident!
– Originally he seemed to have [almost] fully recovered
Bigelow, Henry J. “Dr. Harlow’s case of
recovery from the passage of an iron bar
through the head.” American Journal of
the Medical Sciences, n.s. v.20 (July
1850): 13-22. Available at:
https://cms.www.countway.harvard.edu/w
p/?tag=phineas-gage
• After a few weeks, Phineas exhibited profound personality changes
– This is the first time, researchers have a clear evidence that the
brain is not a continuum of cell mass and rather each region has
relatively independent task
2014
Dept of Comp Med & Bioinf,
Kayvan Najarian
13
Introduction to Connectionist Models (Continued)
• learning and generalization through examples
• simple building block: neuron
– Dendrites: collecting signals from other neurons
– Soma (cell body): spatial summation and processing
– Axon: transmitting signals to dendrites of other cells
2014
Dept of Comp Med & Bioinf,
Kayvan Najarian
14
From biological to artificial neural nets
• Reference book: “Fundamentals of Neural Networks; Architecture,
Algorithms, And Applications”, by: L. Fausett.
• Highly recommended for this course to learn practical applications
of neural nets
• Biological vs. artificial neurons
– From biological neuron to schematic structure of artificial
neuron
• biological:
– Inputs
– Summation
–
–
of inputs
Processing
unit
Output
• artificial:
2014
L. Fausett
Activation function
x1
xN
w1
y  f (w1 x1  ...  wn xn )
wN
Dept of Comp Med & Bioinf,
Kayvan Najarian
15
From biological to artificial neural net (continued)
neuron 1
– Artificial neural nets:
w11
x1
• Single-layer:
neuron 2
w1i
xN
y1
y2
neuron i
yi
wNi
neuron
M-1
neuron
M
wNM
yM 1
yM
y1
w11
• Multi-layer
x1
y2
w1i
xN
wNi
wNM
yi
yM 1
yM
2014
Dept of Comp Med & Bioinf,
Kayvan Najarian
16
A Supervised NN: Backpropagation Neural
Network
•
•
Training: using a set of known examples to estimate best
values of weights (e.g. backpropagation algorithm)
Architecture:
–
•
It was proved that three layers (one input, one hidden and
one output) with sufficient number of neurons in the
hidden layer, and learn practically any function
–
–
•
2014
Number of layers and number of neurons in each layer: variable
As such there is no need to try more than three layers
A rule of thumb suggests that the number of hidden layers must
be less than 1/10 of the number of training examples
Majority of algorithms designed for neural networks are
gradient based
Dept of Comp Med & Bioinf,
Kayvan Najarian
17
Backpropagation Neural Networks (cont’d)
• Another issue that all types of machine learning methods,
including neural networks can suffer from is overfitting
– They can be “over-trained” with the training data and perform
poorly on the data they have not seen before
– A common approach to address this problem is to ensure that the
size of the parameter search space (weight space in case of neural
nets) is reduced
– For instance, to address this issue neural nets, often a term
containing the following value to the cost function to be minimized:
w
2014
2
Dept of Comp Med & Bioinf,
Kayvan Najarian
18
Neural Networks for Clustering
• Artificial competitive neural networks:
– Each artificial neuron (or group of neurons) stores a pattern
– Networks are trained such that neurons in the same neighborhood
store similar patterns
– During classification, neurons compete to relate to the new pattern
– The neurons with highest similarity to the new pattern are the
winners
– The most popular type of unsupervised neural network is Kohonen
Self-Organizing Map (K-map)
– K-maps are heavily used in systems biology and bioinformatics,
e.g. clustering of gene expression data
2014
Dept of Comp Med & Bioinf,
Kayvan Najarian
19
Kohonen Self-Organizing Maps
• Kohonen Self-Organizing Map (Kohonen SOM): most
popular unsupervised learning machine
• Architecture (one-dimensional): (Fausett)
– Input neurons map n-dimensional patterns to output (competitive)
neurons with p-dimensional output patterns
– Output neurons with similar patterns
are arranged to be neighbors
– Some output neurons might
store more than one pattern
2014
Dept of Comp Med & Bioinf,
Kayvan Najarian
20
Kohonen Self-Organizing Maps (continued)
• Example: object classification using one-dimensional array
Inputs
weight (0 to 1)
pencil
texture
(wood=0, metal =1)
size (0 to 1)
flies (1) or not (0)
airplane
chair
book
wooden
house
stapler
metal
desk
truck
airplane
truck
wooden
house
kite
metal
desk
chair
stapler
book
pencil
kite
– New pattern: hovercraft
• is mapped to the nationhood of truck or airplane
– Disadvantage: one-dimensional array positions some objects with some
similarities far from each other
2014
Dept of Comp Med & Bioinf,
Kayvan Najarian
21
Support Vector Machines (SVMs)
• Idea: design classifier such that the margin between
boundaries and instances of the classes is optimal
(maximum)
SVM
classification
boundaries
Different options
of classification
boundaries
Hyperplanes
Tarca AL, Carey VJ, Chen X-w, Romero R, Drăghici S (2007) Machine Learning and Its Applications to
Biology. PLoS Comput Biol 3(6): e116. doi:10.1371/journal.pcbi.0030116
– Having a good margin makes classifier less susceptible to uncertainty and more
likely to learn/generalize the data.
2014
Dept of Comp Med & Bioinf,
Kayvan Najarian
22
SVMs (cont’d)
• Formulation (linear kernel):
x1 , y1 , x2 , y2 ,, x N , yN 
yi   1,1
– Objective: to find w and b such that the hyperplane wxT+b=0
that:
1. Separates all/most of samples in the two classes
2. Maximizes the margin between the classes labeled -1 and 1.
– Without discussing the details of the solutions to this problem:
• This optimization problem can be formulated in at least two different
methods and solved rather effectively
• Decision function:


f (x)  sign (wx T  b)  sign    i yi (x i x T )  b 
 i

• The problem can be easily extended into multi-class classification
scenarios
2014
Dept of Comp Med & Bioinf,
Kayvan Najarian
23
SVMs (cont’d)
• What if the inputs are not linearly separable in the
original feature/input space?
– Inputs in the two regions shown here are separable, by
by a good margin, but lines/hyperplanes are not the
best elements to separate them
• In such cases, we use a kernel that maps the input
space into space that might create better separation
– These kernels are often nonlinear functions with symmetric
properties and with [much] higher dimension that the original
space
– Popular kernels: radial basis functions (RBF) and Gaussian
2014
Dept of Comp Med & Bioinf,
Kayvan Najarian
24
Decision/Regression Trees
• Decision and regression
trees hierarchically create
rules that classify /
analyze data
• They are very popular in
medical applications due
to their transparency
2014
Dept of Comp Med & Bioinf,
Kayvan Najarian
25
Decision/Regression Trees (cont’d)
• A visual example:
Tarca AL, Carey VJ, Chen X-w, Romero R, et al. (2007) Machine Learning and Its Applications to Biology. PLoS Comput Biol 3(6): e116.
doi:10.1371/journal.pcbi.0030116
http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0030116
2014
Dept of Comp Med & Bioinf,
Kayvan Najarian
26
Decision/Regression Trees (cont’d)
• What measure can tell us:
– What variable to branch on next?
– What value for this variable is the threshold for branching
• Although different measures are used for this purpose,
resulting to variety of decision trees, almost all of them are
based on entropy, which is a measure of uncertainty/impurity
E   pi log pi
High
entropy,
high
impurity
i
Low
entropy, low
impurity
• Entropy quantifies lack of “purity” among the examples left
in a given node
2014
Dept of Comp Med & Bioinf,
Kayvan Najarian
27
Decision/Regression Trees (cont’d)
• One typical measure used for splitting nodes; information
gain:
Information Gain = Entropy(parent) – [Average Entropy(children)]
• Unlike connectionist methods, dealing with categorical
variables in the nature of decision trees
• There are many tree-based methods such as ID3, CART
(Classification and Regression Tree) and C4.5
• Decision/regression trees can overfit the data, in particular
when depth of the tree becomes too large
– Pruning is used to partially address this issue; trees are first expanded
to large depth and then pruned/collapsed according to some quality
measure
2014
Dept of Comp Med & Bioinf,
Kayvan Najarian
28
Random Forest
• Another solution to address the issue of overfitting when
dealing with trees using bootstrapping / bagging
• Data are randomly split into subsets
• Random subsets of input variables are formed
– This allows a level of variable/feature selection not available in
many other machine learning models
• Using subsets of data and subsets of input variables, trees
are forms
• Performance of these trees are tested using the data not
seen by those trees
– This is a level of validation not available in many other treebased methods
2014
Dept of Comp Med & Bioinf,
Kayvan Najarian
29
Random Forest (cont’d)
• Finally, the output of random forest to a new input will be
the average of the output of all trees to that input
• Random forest is known to have good accuracy without
serious overfitting
• Also, it is one of the fastest machine learning methods given
its desirable performance
• Furthermore, since a level of feature selection is conducted
by Random Forest, it may be applied to some datasets large
number of input features without feature selection
• It was shown, at least in some microarray based studies, that
on average Random Forest might produce the best results for
bioinformatics applications
2014
Dept of Comp Med & Bioinf,
Kayvan Najarian
30
Testing and Validation of Machine Learning
Models
• There are two main approaches:
1.
Training-testing: Randomly divide data into training and testing sets, and
test the performance on the testing data.
One approach
Training
Another
approach
Training
2.
Testing
Validation /
Tune-up
Testing
n-fold cross validation: Randomly divide data into n folds (often n=10) and
in a “round-robin” like approach, train the model using n-1 folds and test on
the nth. The average the performance over all n trained models.
n=4
2014
Dept of Comp Med & Bioinf,
Kayvan Najarian
31
Testing and Validation of Machine Learning
Models (cont’d)
–
–
•
An extreme but special case of n-fold cross validation is called
“leave-one-out” in which for each of the round-robin attempts, all
but one example is training and that example is used for testing
If the number of examples is small, leave-one-out is a reasonable
option; if not, n-fold cross validation is preferred because it is less
likely to overfit the data
Performance measures
–
–
–
Regardless of specific approach used for testing and validation, some
popular measures are used for evaluating the goodness of classification
These measures are evaluated based on “confusion matrix”
When diagonal elements are large,
Class Positive
Class Negative
and others are small,
Predicted as Positive True Positive
False Positive
life is beautiful!
Predicted as Negative
2014
Dept of Comp Med & Bioinf,
Kayvan Najarian
False Negative
True Negative
32
Testing and Validation of Machine Learning
Models (cont’d)
–
Some important measures based on confusion matrix:
Accuracy 
True Positive  True Negative
True Predictions

True Positive  True Negative  False Positive  False Negative
All Predictions
Sensitivity  Re call  True Positive Rate 
Specificit y 
True Negative
True Negative

True Negative  False Positive Negative Class
Precision  Positive Predictive Value 
True Positive
True Positive

True Positive  False Positive Predicted as Positive
False Positive Rate  1  Specificit y 
2014
True Positive
True Positive

True Positive  False Negative Positive Class
False Positive
False Positive

Faslse Positive  True Negative Negative Class
Dept of Comp Med & Bioinf,
Kayvan Najarian
33
Testing and Validation of Machine Learning
Models (cont’d)
–
For about the same accuracy, machine learning classes can be
trained to have a different balance between true sensitivity and
specificity; or equivalently the balance between false positive rate
(FPR) and true positive rate (TPR)
•
–
&
TPR = Sensitivity
Receiver operating characteristic (ROC) curve is measure to show
the trade-off between FPR and TPR
•
–
Different threshold values or weighting on
cost functions are used to generate points in ROC
A good ROC is the one that rises early so that high
sensitivity and specificity are achieved at the same time
1=
Sensitivity
(=TPR)
•
1-specificity (=FPR)
Area Under Curve (AUC) of ROC
•
2014
Remember: FPR=1-Specificity
A measure of how fast ROC rises and how soon a good balance point between
specificity and sensitivity is achieved
Dept of Comp Med & Bioinf,
Kayvan Najarian
34
Feature Reduction / Selection
•
•
Fewer features reduces the computational complexity and
likelihood of overfitting
There are three main approaches to reduce the number of
features:
1.
Using domain knowledge to select some of the most relevant
features
Computationally mixing all features to generate fewer combined
features (such as PCA)
Computationally selecting a smaller set using a criterion / ranking
system
2.
3.
•
•
2014
These methods in turn divide into filter-based and wrapper-based methods
Typical measures/criteria used for this process include information gain
Dept of Comp Med & Bioinf,
Kayvan Najarian
35
Summary
• Machine learning applied on molecular / cellular data,
along with other types of data, would allow system
biologic study of the system
• Clustering (unsupervised learning) and classification
(supervised learning) are the two main tasks in machine
learning
• Multilayer perceptron neural networks, support vector
machines and regression tress are the main techniques
used for classification
– Many techniques are based on these methods, e.g. Random
Forest is a method based on collective decision of a number of
tress
2014
Dept of Comp Med & Bioinf,
Kayvan Najarian
36
Summary
• Machine learning models are susceptible to overfitting
issue
• Methods such as n-fold cross validation are used for
testing and validation of machine learning models
• There is often need to reduce dimensionality of data
• A number of measures such as sensitivity and specificity
are used to assess the quality of a model
2014
Dept of Comp Med & Bioinf,
Kayvan Najarian
37